A new algorithm for clustering based on kernel density estimation

In this paper, we present an algorithm for clustering based on univariate kernel density estimation, named ClusterKDE. It consists of an iterative procedure that in each step a new cluster is obtained by minimizing a smooth kernel function. Although in our applications we have used the univariate Gaussian kernel, any smooth kernel function can be used. The proposed algorithm has the advantage of not requiring a priori the number of cluster. Furthermore, the ClusterKDE algorithm is very simple, easy to implement, well-defined and stops in a finite number of steps, namely, it always converges independently of the initial point. We also illustrate our findings by numerical experiments which are obtained when our algorithm is implemented in the software Matlab and applied to practical applications. The results indicate that the ClusterKDE algorithm is competitive and fast when compared with the well-known Clusterdata and K-means algorithms, used by Matlab to clustering data.     

A robust automatic clustering algorithm for probability density functions with application to categorizing color images

This study develops a robust automatic algorithm for clustering probability density functions based on the previous research. Unlike other existing methods that often pre-determine the number of clusters, this method can self-organize data groups based on the original data structure. The proposed clustering method is also robust in regards to noise. Three examples of synthetic data and a real-world COREL dataset are utilized to illustrate the accurateness and effectiveness of the proposed approach.     

城市人口密度、国内市场规模与就业增长

我国经济“高增长、低就业”现象的原因在于我国贸易成本过高，国内市场规模较少。解决我国就业问题的关键在于减少行政干预，顺应市场要求，促进人口在空间上的适度集中，提高人口密度，提高消费效率，扩大市场规模。应进一步完善城乡一体的户籍制度，完善整合城乡劳动力市场，提高要素流动能力等。     

Closed-form likelihood estimation for one type of affine point processes

ABSTRACT

This paper presents a closed-form likelihood approximation for one type of affine point processes widely used in financial credit risk models. We proceed by first conjecturing the concrete series form of the transition density, verifying our postulation and then establishing the related coefficients by means of Kolmogorov equations. The asymptotic properties of the maximum-likelihood estimators (MLEs) are given in the end.     

A New Quantile Function with Applications to Reliability Analysis

In this article, we propose a new class of distributions defined by a quantile function, which nests several distributions as its members. The quantile function proposed here is the sum of the quantile functions of the generalized Pareto and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. The estimation of the parameters of the model using L-moments is studied. Finally, we apply the model to a real life dataset.     

Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.     

中国生产性服务业TFP的时空差异与影响因素分析

在利用Malmquist指数法测算2005-2013年中国30个省份生产性服务业的全要素生产率(TFP)的基础上,采用核密度估计法分析了TFP的动态演变,并运用分位数回归方法对中国生产性服务业TFP的影响因素进行了实证分析。研究发现:在考察期内中国生产性服务业TFP总体呈下降态势,技术效率下降是其下降的主要原因;核密度曲线说明中国生产性服务业TFP省际差距扩大,技术效率和技术进步逐渐呈现两极分化的趋势;分位数回归结果表明,工业化水平和人力资本水平对生产性服务业TFP提升具有普遍的促进作用,而信息化水平、对外开放水平、制造业集中度对生产性服务业TFP提高的贡献大小均与地区生产性服务业TFP的水平有关。     

Tempered Mittag-Leffler Lévy processes

In this article, we introduce tempered Mittag-Leffler Lévy processes (TMLLP). TMLLP is represented as tempered stable subordinator delayed by a gamma process. Its probability density function and Lévy density are obtained in terms of infinite series and Mittag-Leffler function, respectively. Asymptotic forms of the tails and moments are given. A step-by-step procedure of the parameters estimation and simulation of sample paths is given. We also provide main results available for Mittag-Leffler Lévy processes (MLLP) and some extensions which are not available in a collective way in a single article. Our results generalize and complement the results available on Mittag-Leffler distribution and MLLP in several directions. Further, the asymptotic forms of the moments of the first-exit times of the TMLLP are also discussed.     

Subsampling-extrapolation bandwidth selection in bivariate kernel density estimation

This paper focuses on bivariate kernel density estimation that bridges the gap between univariate and multivariate applications. We propose a subsampling-extrapolation bandwidth matrix selector that improves the reliability of the conventional cross-validation method. The proposed procedure combines a U-statistic expression of the mean integrated squared error and asymptotic theory, and can be used in both cases of diagonal bandwidth matrix and unconstrained bandwidth matrix. In the subsampling stage, one takes advantage of the reduced variability of estimating the bandwidth matrix at a smaller subsample size m (m < n); in the extrapolation stage, a simple linear extrapolation is used to remove the incurred bias. Simulation studies reveal that the proposed method reduces the variability of the cross-validation method by about 50% and achieves an expected integrated squared error that is up to 30% smaller than that of the benchmark cross-validation. It shows comparable or improved performance compared to other competitors across six distributions in terms of the expected integrated squared error. We prove that the components of the selected bivariate bandwidth matrix have an asymptotic multivariate normal distribution, and also present the relative rate of convergence of the proposed bandwidth selector.     

Non-parametric estimation of reciprocal coordinate subtangent for right censored dependent scheme

The concept of reciprocal coordinate subtangent (RCST) has been used as a useful tool to study the monotone behavior of a continuous density function and for characterizing probability distributions. In this paper, we propose a non-parametric estimator for RCST based on the censored dependent data. Asymptotic properties of the estimator are established under suitable regularity conditions. A simulation study is carried out to examine the performance of the estimator. The usefulness of the estimator is also examined through a real data.